A237929 Numbers n such that (i) the sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1, and (ii) n and n+1 have the same number of prime divisors (with repetition).

2, 9, 98, 170, 1274, 4233, 4345, 7105, 7625, 14905, 21385, 30457, 34945, 66585, 69874, 77314, 82946, 98841, 175354, 177122, 233090, 236282, 238017, 263145, 265225, 295274, 298082, 322234, 335793, 336106

Offset

1,1

Comments

The first term a(1)=2 is the only prime number in this sequence.

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..96049

Example

For n=98: prime factors = 2,7,7; sum of prime factors = 16; number of prime divisors = 3
For n+1=99: prime factors = 3,3,11; sum of prime factors = 17; number of prime divisors=3.

Mathematica

Select[Partition[Table[{n, PrimeOmega[n], Total[Times@@@FactorInteger[n]]}, {n, 34*10^4}], 2, 1], #[[1, 2]]==#[[2, 2]]&&#[[1, 3]]+1==#[[2, 3]]&][[;; , 1, 1]] (* Harvey P. Dale, May 03 2024 *)

Prog

(Python)
## sumdivisors(n) is a function that would return the sum of prime
## divisors of n
## numdivisors(n) is a function that would return the number of prime
## divisors of n
i=2
while i < 100000:
..sdi=sumdivisors(i)
..sdip=sumdivisors(i+1)
..ndi=numdivisors(i)
..ndip=numdivisors(i+1)
..if sdi==sdip-1 and ndi==ndip:
....print i, i+1
..i=i+1

Crossrefs

Cf. A001414, A006145 Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.

Cf. A228126 Sum of prime divisors of n (with repetition) is one less than the sum of prime divisors (with repetition) of n+1.

Cf. A045920 Numbers n such that factorizations of n and n+1 have same number of primes (including multiplicities).

Sequence in context: A013132 A317275 A013057 * A227258 A027686 A360696

Adjacent sequences: A237926 A237927 A237928 * A237930 A237931 A237932

Keyword

nonn

Author

Abhiram R Devesh, Feb 16 2014

Status

approved